msPCA: An R Package for Sparse PCA with Multiple Components

2026-07-06

AI Summary

This study addresses the challenge that traditional sparse principal component analysis (PCA) struggles to simultaneously achieve high explained variance, sparsity, and non-redundancy among multiple principal components in high-dimensional data. To overcome this limitation, the authors propose msPCA, a novel method based on an alternating maximization algorithm that enforces two forms of non-redundancy constraints—either orthogonality of loadings or zero correlation among principal components—while preserving high variance explanation and sparsity. The accompanying open-source R package efficiently scales to datasets with thousands of features, demonstrating superior performance over existing approaches by striking an effective balance between controllable sparsity and computational efficiency.

Abstract

We present msPCA: an open-source R package for sparse principal component analysis with multiple components. It implements an alternating maximization algorithm to generate a set of sparse loading vectors that collectively explain a large fraction of the variance in a dataset, while remaining non-redundant. The algorithm supports two definitions of non-redundancy: either orthogonality of the loading vectors or zero pairwise correlation between principal components (PCs). In the reported benchmarks, msPCA solves sparse PCA problems with thousands of features, achieving competitive runtimes while producing sparse components with controlled feasibility violations and a high fraction of variance explained.

Problem

• sparse PCA
• multiple components
• non-redundancy
• variance explained
• loading vectors

Innovation

• sparse PCA
• multiple components
• alternating maximization
• non-redundancy
• R package